Implementation of Adjacency List

Adjacency List can be implemented in Java using collections like HashMap for mapping vertices to their adjacent vertices and LinkedList or ArrayList for storing the adjacent vertices.

Basic Operations

1. Add Vertex: This operation can add a new vertex to the graph. A vertex can represents the node in the graph and adding the vertex means adding the new entity into the graph without any connections to the other vertices.
2. Add Edge: This operation can add a new edge between the two vertices in the graph. An Edge can represent the connection between the two vertices. Adding the edge establishes the link between the two vertices and it can be allowing the traversal between them.
3. Remove Vertex: This operation can remove the vertex and all its incident edges from the graph. Removing the vertex eliminates it from the graph.
4. Remove Edge: This operation can remove the edge between the two vertices in the graph. Removing the edge is the connection between the two vertices without affecting the vertices.
5. Find Neighbors: This operation can retrieve the list of the neighbours (adjacent vertices) of the given vertex. Neighbours are vertices directly connected to a particular vertex via an edge.
6. Print Graph: This operation can be used to prints the entire graph with its vertices and their corresponding adjacency lists. Printing the graph allows the visualizing the structure of the graph.

Adjacency List is the data structure used to represent graphs which can consist of the vertices(nodes) and the edges(connections between the nodes). In the adjacency list, each vertex is associated with the list of its neighbouring vertices. This data structure is most commonly used to efficiently represent sparse graphs where the number of edges is much smaller than the number of possible edges.